Neutrino splitting for Lorentz-violating neutrinos: Detailed analysis

Abstract

Lorentz-violating neutrino parameters have been severely constrained on the basis of astrophysical considerations. In the high-energy limit, one generally assumes a superluminal dispersion relation of an incoming neutrino of the form E ≈ | p| v, where E is the energy, p is the momentum and v = √ 1 + δ > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (ν → ν + e − + e + ) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter δ can be derived. Here, we investigate a related process, νi → νi + ν f + ν f , where νi is an incoming neutrino mass eigenstate, while ν f is the final neutrino mass eigenstate, with a superluminal velocity that is slightly slower than that of the initial state. This process is kinematically allowed if the Lorentz-violating parameters at high energy differ for the different neutrino mass eigenstates. Neutrino splitting is not subject to any significant energy threshold condition and could yield quite a substantial contribution to decay and energy loss processes at high energy, even if the differential Lorentz violation among neutrino flavors is severely constrained by other experiments. We also discuss the SU (2)L-gauge invariance of the superluminal models and briefly discuss the use of a generalized vierbein formalism in the formulation of the Lorentz-violating Dirac equation.

Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector with Additional Decay Channels

“…For δ i = δ f , no phase space is available in order to accommodate for the decay. This consideration explains why all results communicated in reference [51] display a factor δ i − δ f ; decay takes place from "faster" to "slower" mass eigenstates.…”

“…The threshold condition E th = 2m f / √ δ i has been used extensively in references [49][50][51]. Equation 3implies that the threshold for NPCR is lower by at a least six orders of magnitude as compared to LPCR.…”

“…The understanding of decay processes involving Lorentz-violation has been advanced through references [49][50][51]. Let us briefly recall elements of the derivation given in reference [51]. One particular question is how to express the decay rate for an (initially) flavor-eigenstate neutrino (the electroweak Lagrangian is flavor-diagonal) in terms of mass eigenstates.…”

“…One particular question is how to express the decay rate for an (initially) flavor-eigenstate neutrino (the electroweak Lagrangian is flavor-diagonal) in terms of mass eigenstates. We have, in the same obvious notation as used in reference [51],…”

“…Cohen and Glashow [49] set v int = 1. (In reference [51], on a number of occasions, the parameter used in reference [49] had been inadvertently indicated as v int = 0, which is not the case. We take the opportunity to point out that of course, the parameter v int = 1 implies that δ int = 0, which was the intended statement in reference [49].)…”